I walked into my room earlier today and couldn't find my adapter for my iPhone 5s, and my little brother turned out to have an identical adapter in his pocket, and he insists it's his for his 7th generation iPod nano, but we have no way to tell who' s it really is. Basically, I'm wondering what the model number is for the adapter for each of these devices, and what any other identifying factors might be.

Sure. It is just a power adapter, with a very standard output, 5.1V,1.0A. It is comparable on almost ALL devices, if there is a corresponding cord. As long as it fits into the wall socket and the end of the cord, it can charge anything.

Well, it is just a common power adapter, and just as any other ones on the market, they work alike. If you get the cord, then sure, you can. However, if you feel the plug becoming hot (not warm, like 100*F, I will suggest you stop using this one and look for one that is with higher output current. Like the standard Apple one with 5.1V, 2.1A output VIA standard USB.
COME ON, it is just a power adapter.

NO. In my opinion, such a small difference (6 per second) should be nothing to the transformer inside. Plus, when I was in china, the 50Hz 20V AC power didn't did any damage to the plug, and I am still using that plug to charge my Powerbanks, and there is(if there is, I cannot either hear it nor observe it.) Also, think that it is labeled 50Hz~60Hz, if what I remembered is not wrong.
All in all, it is totally OK.

Basically zero. I had mine plugged into a kill-a-watt meter and it doesn't even register when the device isn't connected. This means that if it draws anything, it's less than 1 watt (which is negligible).

Bill. The answer is "not really". Though the output from an iPhone charger is 5VDc, it can only give 5 Watts power. Voltage and power are different things. You may be using 5VDc, but if your device needs more than 5 Watts, then one of two things may happen.
1. Your device may not work, or work at a reduced capacity. E.g. a light would not be as bright as expected.
2. You will cause a larger power draw than the iPhone charger can handle and may either cause the charger to fail, or worst case a fire.
Please get the correct item charger for your device or go into somewhere like Maplin, with your device and they will keep you right.